Resilient Strong Structural Controllability of Leader–Follower Networks via Edge Augmentation

Leader–follower networks are widely used to control large-scale multi-agent systems with reduced actuation and communication requirements. In such networks, strong structural controllability provides a graph-theoretic framework to guarantee controllability independently of precise system parameters. However, strong structural controllability may be compromised by malfunctions affecting agents or communication links, which motivates the study of resilience. This paper investigates resilient strong structural controllability of leader–follower networks and addresses the problem of enhancing resilience through graph modifications while maintaining a fixed set of leaders. Conditions are derived under which the addition of an edge guarantees an improvement of resilience for a follower node. It is shown that edge additions that locally enhance resilience may, in certain cases, degrade resilience elsewhere in the network. To address this issue, a sufficient condition is established which ensures that edge additions lead exclusively to an improvement of resilient controllability at the network level. The results offer a graph-theoretic approach to enhancing resilience while avoiding an increasing number of leaders, and the method is particularly suited for networks with structurally vulnerable regions.